Integro-differential equations and functional analysis

About formal normal form of the semi-hyperbolic maps germs on the plane

P. A. Shaikhullina

Chelyabinsk State University, Chelyabinsk, Russian Federation

Abstract: There are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or one). In this paper, the first stage of constructing an analytical classification by the method of functional invariants is carried out: a theorem on the reducibility of a germ to its formal normal form by «semiformal» changes of coordinates is proved. The one-time shift along the saddle-node vector field (the formal normal form in the problem of the analytical classification of saddle-node vector fields on a plane) is chosen as the formal normal form.

Keywords: semi-hyperbolic maps, formal classification, analytical classification.

UDC: 517.938

MSC: 34M35, 34M40

Received: 29.10.2021

DOI: 10.26516/1997-7670.2021.38.54

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